diff --git a/news/changelog-1.6.md b/news/changelog-1.6.md
index cd3f508dc2c..d6f820934fb 100644
--- a/news/changelog-1.6.md
+++ b/news/changelog-1.6.md
@@ -71,6 +71,7 @@ All changes included in 1.6:
 ## Projects
 
 - ([#10268](https://github.com/quarto-dev/quarto-cli/issues/10268)): `quarto create` supports opening project in Positron, in addition to VS Code and RStudio IDE.
+- ([#10566](https://github.com/quarto-dev/quarto-cli/issues/10566)): Ensure that `quarto run` outputs `stdout` and `stderr` to the correct streams.
 
 ### Websites
 
diff --git a/src/core/run/lua.ts b/src/core/run/lua.ts
index 6c5fbdf70b9..d9e797ed274 100644
--- a/src/core/run/lua.ts
+++ b/src/core/run/lua.ts
@@ -42,10 +42,16 @@ export const luaRunHandler: RunHandler = {
     );
     cmd.push(...args);
 
-    return await execProcess({
-      cmd,
-      ...options,
-    }, "");
+    return await execProcess(
+      {
+        cmd,
+        ...options,
+      },
+      "",
+      undefined,
+      undefined,
+      true,
+    );
   },
 };
 
diff --git a/src/core/run/python.ts b/src/core/run/python.ts
index 3770adf166b..1fda17f5fb9 100644
--- a/src/core/run/python.ts
+++ b/src/core/run/python.ts
@@ -1,9 +1,8 @@
 /*
-* python.ts
-*
-* Copyright (C) 2020-2022 Posit Software, PBC
-*
-*/
+ * python.ts
+ *
+ * Copyright (C) 2020-2022 Posit Software, PBC
+ */
 
 import { extname } from "../../deno_ral/path.ts";
 import { pythonExec } from "../jupyter/exec.ts";
@@ -21,13 +20,19 @@ export const pythonRunHandler: RunHandler = {
     stdin?: string,
     options?: RunHandlerOptions,
   ) => {
-    return await execProcess({
-      cmd: [
-        ...(await pythonExec()),
-        script,
-        ...args,
-      ],
-      ...options,
-    }, stdin);
+    return await execProcess(
+      {
+        cmd: [
+          ...(await pythonExec()),
+          script,
+          ...args,
+        ],
+        ...options,
+      },
+      stdin,
+      undefined,
+      undefined,
+      true,
+    );
   },
 };
diff --git a/src/core/run/r.ts b/src/core/run/r.ts
index 98b3eec47be..185bfe1a15d 100644
--- a/src/core/run/r.ts
+++ b/src/core/run/r.ts
@@ -1,9 +1,8 @@
 /*
-* r.ts
-*
-* Copyright (C) 2020-2022 Posit Software, PBC
-*
-*/
+ * r.ts
+ *
+ * Copyright (C) 2020-2022 Posit Software, PBC
+ */
 
 import { extname } from "../../deno_ral/path.ts";
 
@@ -21,13 +20,19 @@ export const rRunHandler: RunHandler = {
     stdin?: string,
     options?: RunHandlerOptions,
   ) => {
-    return await execProcess({
-      cmd: [
-        await rBinaryPath("Rscript"),
-        script,
-        ...args,
-      ],
-      ...options,
-    }, stdin);
+    return await execProcess(
+      {
+        cmd: [
+          await rBinaryPath("Rscript"),
+          script,
+          ...args,
+        ],
+        ...options,
+      },
+      stdin,
+      undefined,
+      undefined,
+      true,
+    );
   },
 };
diff --git a/tests/smoke/run/run-script.test.ts b/tests/smoke/run/run-script.test.ts
index 0d62a71c8a8..2a7ab6ee943 100644
--- a/tests/smoke/run/run-script.test.ts
+++ b/tests/smoke/run/run-script.test.ts
@@ -1,14 +1,53 @@
 import { basename, join } from "../../../src/deno_ral/path.ts";
 import { ensureDirSync } from "../../../src/deno_ral/fs.ts";
-import { assert } from "testing/asserts";
+import { assert, assertEquals } from "testing/asserts";
 import { execProcess } from "../../../src/core/process.ts";
 import { quartoDevCmd } from "../../utils.ts";
 import { unitTest } from "../../test.ts";
+import { EOL } from "fs/eol";
+import { lines } from "../../../src/core/text.ts";
 
 const workingDir = Deno.makeTempDirSync();
 
 ensureDirSync(workingDir);
 
+const ensureStreams = (name: string, script: string, stdout: string, stderr: string) => {
+  unitTest(name, async () => {
+    const result = await execProcess({
+        cmd: [
+          quartoDevCmd(),
+          "run",
+          basename(script),
+        ],
+        // disable logging here to allow for checking the output
+        env: {
+          "QUARTO_LOG_LEVEL": "CRITICAL",
+        }
+      },
+      undefined,
+      undefined,
+      undefined,
+      true
+    );
+    assert(result.success);
+    assertEquals((result.stdout ?? "").replaceAll("\r", ""), stdout);
+    assertEquals((result.stderr ?? "").replaceAll("\r", ""), stderr);
+  }, 
+  {
+    teardown: () => {
+      try {
+        Deno.removeSync(basename(script));
+      } catch (_e) {
+        // ignore
+      }
+      return Promise.resolve();
+    },
+    cwd: () => {
+      return workingDir;
+    }
+  })
+}
+
 const testRunCmd = (name: string, script: string) => {
   unitTest(name, async () => {
     const result = await execProcess({
@@ -16,7 +55,7 @@ const testRunCmd = (name: string, script: string) => {
         quartoDevCmd(),
         "run",
         basename(script),
-      ],
+      ]
     });
     assert(result.success);
   }, 
@@ -53,4 +92,26 @@ testRunCmd("run-py-script", pyScript);
 // Run R script
 const rScript = join(workingDir, "test.R");
 Deno.writeTextFileSync(rScript, "print('Hello, world!')");
-testRunCmd("run-r-script", rScript);
\ No newline at end of file
+testRunCmd("run-r-script", rScript);
+
+// check stream outputs
+
+// in R
+const rScript2 = join(workingDir, "test2.R");
+Deno.writeTextFileSync(rScript2, "cat('write stdout\\n', file = stdout()); cat('write stderr\\n', file = stderr())");
+ensureStreams("run-r-script-stdout-stderr", rScript2, "write stdout\n", "write stderr\n");
+
+// in Python
+const pyScript2 = join(workingDir, "test2.py");
+Deno.writeTextFileSync(pyScript2, "import sys; print('write stdout'); print('write stderr', file = sys.stderr)");
+ensureStreams("run-py-script-stdout-stderr", pyScript2, "write stdout\n", "write stderr\n");
+
+// in Deno TS
+const tsScript2 = join(workingDir, "test2.ts");
+Deno.writeTextFileSync(tsScript2, "console.log('write stdout'); console.error('write stderr')");
+ensureStreams("run-ts-script-stdout-stderr", tsScript2, "write stdout\n", "write stderr\n");
+
+// in Lua
+const luaScript2 = join(workingDir, "test2.lua");
+Deno.writeTextFileSync(luaScript2, "print('write stdout'); io.stderr:write('write stderr\\n')");
+ensureStreams("run-lua-script-stdout-stderr", luaScript2, "write stdout\n\n", "write stderr\n"); // don't know why there is an extra newline
\ No newline at end of file